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Two-dimensional resonant triad interactions in a two-layer system
We consider resonant triad interactions between surface and internal gravity waves propagating in two horizontal dimensions in a two-layer system with a free surface. As the system supports both surface and internal wave modes, two different types of resonant triad interactions are possible: one wit...
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Published in: | Journal of fluid mechanics 2021-01, Vol.907, Article A5 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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Summary: | We consider resonant triad interactions between surface and internal gravity waves propagating in two horizontal dimensions in a two-layer system with a free surface. As the system supports both surface and internal wave modes, two different types of resonant triad interactions are possible: one with two surface and one internal wave modes and the other with one surface and two internal wave modes. The resonance conditions are studied in detail over a wide range of physical parameters (density and depth ratios). Explicitly identified are the spectral domains of resonance whose boundaries represent one-dimensional resonances (class I–IV). To study the nonlinear interaction between two-dimensional surface and internal waves, a spectral model is derived from an explicit Hamiltonian system for a two-layer system after decomposing the surface and interface motions into the two wave modes through a canonical transformation. For both types of resonances, the amplitude equations are obtained from the reduced Hamiltonian of the spectral model. Numerical solutions of the explicit Hamiltonian system using a pseudo-spectral method are presented for various resonance conditions and are compared with those of the amplitude equations. |
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ISSN: | 0022-1120 1469-7645 |
DOI: | 10.1017/jfm.2020.824 |